How to update a run cycle custom animation?

If I am walking and then I hold shift, I am suppose to start running and the running animation starts playing instead. But what actually happens is when I am walking and then I hold shift I start running but the running animation will not start playing until I stop running for a moment while also holding shift and then running again because the animation is still on the walking animation at the start since it loops forever until you stop walking. How can I make it change instantly instead of having to stop and start again to start the correct animation?

Local Script, Located in PlayerScripts:

Players = game:GetService("Players")
LocalPlayer = Players.LocalPlayer
userInput = game:GetService("UserInputService")

sprinting = false

userInput.InputBegan:Connect(function(key)
	if key.KeyCode == Enum.KeyCode.LeftShift or key.KeyCode == Enum.KeyCode.RightShift then
		sprinting = true
		game.ReplicatedStorage.Sprint:FireServer(LocalPlayer)
	end
end)


userInput.InputEnded:Connect(function(key)
	if key.KeyCode == Enum.KeyCode.LeftShift or key.KeyCode == Enum.KeyCode.RightShift then
		sprinting = false
		game.ReplicatedStorage.Walk:FireServer(LocalPlayer)
	end
end)

Server Script, located in server script service:

game.ReplicatedStorage.Sprint.OnServerEvent:Connect(function(player)
	player.Character.Humanoid.WalkSpeed = 25
	player.Character.Animate.walk.WalkAnim.AnimationId = "rbxassetid://4920166649"
	player.Character.Animate.run.RunAnim.AnimationId = "rbxassetid://4920166649"
end)

game.ReplicatedStorage.Walk.OnServerEvent:Connect(function(player)
	player.Character.Humanoid.WalkSpeed = 16
	player.Character.Animate.walk.WalkAnim.AnimationId = "rbxassetid://4919640169"
	player.Character.Animate.run.RunAnim.AnimationId = "rbxassetid://4919640169"
end)